Non-equilibrium thermionic electron emission for metals at high temperatures

TL;DR

This paper introduces a non-equilibrium quantum Kappa distribution model to accurately predict thermionic electron emission from heated metals at high temperatures, extending classical laws and quantifying deviations from equilibrium.

Contribution

It develops an analytical model based on a non-equilibrium quantum Kappa distribution to describe thermionic emission, improving predictions at high temperatures.

Findings

Accurately predicts thermionic currents across temperature ranges.

Shows high-energy tail increases emission beyond classical predictions.

Quantifies departure from Fermi-Dirac statistics.

Abstract

The stationary thermionic electron emission currents from heated metals are compared against an analytical expression derived using a non equilibrium quantum Kappa energy distribution for the electrons. This later depends on the temperature decreasing parameter $\kappa(T)$ which can be estimated from the raw experimental data and characterizes the departure of the electron energy spectrum from the equilibrium Fermi-Dirac statistics. The calculations accurately predict the measured thermionic emission currents for both high and moderate temperature ranges. The Richardson-Dushman law governs the electron emission for large values of Kappa or equivalently, for moderate metal temperatures. The high energy tail in the electron energy distribution function which develops at higher temperatures or lower Kappa parameters, increases the emission currents well over the predictions of the classical expression. This analysis also permits the quantitative estimation of the departure of the metal electrons from the equilibrium Fermi-Dirac statistics.